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<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>28</B></div> <div> <B>Suma y resta combinadas de polinomios con coeficientes enteros</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>Procedimiento </B></div> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Se ordenan los polinomios</FONT></div> <div> <B>2.</B> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > Se identifican los polinomios tanto del minuendo como del sustraendo</FONT></div> <div> <B>3.</B> <FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > Se efectúa la suma de los polinomios que hacen parte del minuendo o del sustraendo, según el caso</FONT></div> <div> <B>4.</B><FONT SIZE="4" COLOR="#000080" FACE="Times New Roman" >  </FONT><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >Se escribe el sustraendo, cada término con signo cambiado, debajo del minuendo y, los términos semejantes compartiendo columna</FONT></div> <div> <B>5.</B> <FONT SIZE="4" COLOR="#000080" FACE="Times New Roman" > </FONT><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >Se efectúa la suma indicada</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los ejercicios</B></div> <bR> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dc96f180.gif" border=0 width="623" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#1" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/lBwuEcTBd34?t=57s" TARGET="_top" TITLE="https://youtu.be/lBwuEcTBd34?t=57s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcac1140.gif" border=0 width="705" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#2" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/lBwuEcTBd34?t=3m25s" TARGET="_top" TITLE="https://youtu.be/lBwuEcTBd34?t=3m25s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcbc1180.gif" border=0 width="705" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#3" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/lBwuEcTBd34?t=5m21s" TARGET="_top" TITLE="https://youtu.be/lBwuEcTBd34?t=5m21s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcc61180.gif" border=0 width="609" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#4" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/67NbReV8TKw" TARGET="_top" TITLE="https://youtu.be/67NbReV8TKw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcd7d140.gif" border=0 width="893" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#5" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/CKBrjfiPZbA" TARGET="_top" TITLE="https://youtu.be/CKBrjfiPZbA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcea3180.gif" border=0 width="931" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#6" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/X3LyGw7p4Wg" TARGET="_top" TITLE="https://youtu.be/X3LyGw7p4Wg"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dcf831b0.gif" border=0 width="899" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#7" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/h88ja4qsnw4" TARGET="_top" TITLE="https://youtu.be/h88ja4qsnw4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dd0f32f0.gif" border=0 width="755" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#8" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/QCqCIDlYTaE" TARGET="_top" TITLE="https://youtu.be/QCqCIDlYTaE"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dd1a02f0.gif" border=0 width="672" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#9" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/7BWilsJwj8Y" TARGET="_top" TITLE="https://youtu.be/7BWilsJwj8Y"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dd26b1c0.gif" border=0 width="875" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#10" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/0-jalRp0WPo" TARGET="_top" TITLE="https://youtu.be/0-jalRp0WPo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dd38c1b0.gif" border=0 width="652" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#11" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/h-Vc0q2wzKc" TARGET="_top" TITLE="https://youtu.be/h-Vc0q2wzKc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="3" COLOR="#000080" FACE="Times New Roman" ><IMG SRC="6dd4d82f0.gif" border=0 width="728" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#12" TITLE="28"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/dM_tBO8VnJ4" TARGET="_top" TITLE="https://youtu.be/dM_tBO8VnJ4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6dd5841b0.gif" border=0 width="900" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/mudWqFS_8SI" TARGET="_top" TITLE="https://youtu.be/mudWqFS_8SI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="6dd674310.gif" border=0 width="628" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/DfC4EfUBlzY" TARGET="_top" TITLE="https://youtu.be/DfC4EfUBlzY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="6dd71f2c0.gif" border=0 width="799" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/SzshXhlwSB0" TARGET="_top" TITLE="https://youtu.be/SzshXhlwSB0"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="6dd8b72f0.gif" border=0 width="695" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/YoO8a5tJfUo" TARGET="_top" TITLE="https://youtu.be/YoO8a5tJfUo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <div> La suma y resta combinadas de polinomios con coeficientes enteros es una operación algebraica que se utiliza para simplificar expresiones y resolver ecuaciones. Cuando hay varios polinomios que constituyen el minuendo y varios polinomios que constituyen el sustraendo, el proceso para realizar esta operación es un poco más complejo pero sigue siendo sencillo de entender.</div> <bR> <div> Primero, se deben sumar todos los polinomios que constituyen el minuendo. Para hacer esto, se deben identificar los términos semejantes (es decir, aquellos que tienen la misma variable elevada al mismo exponente) en cada uno de los polinomios y sumar sus coeficientes correspondientes. Una vez que se han sumado todos los términos semejantes en cada uno de los polinomios del minuendo, se obtiene un nuevo polinomio que representa la suma de todos ellos.</div> <bR> <div> Luego, se deben sumar todos los polinomios que constituyen el sustraendo siguiendo el mismo proceso: identificando los términos semejantes y sumando sus coeficientes correspondientes. Una vez que se han sumado todos los términos semejantes en cada uno de los polinomios del sustraendo, se obtiene un nuevo polinomio que representa la suma de todos ellos.</div> <bR> <div> Por último, para obtener el resultado final de la operación de suma y resta combinadas de polinomios con coeficientes enteros, se debe restar el resultado del sustraendo al resultado del minuendo. Para hacer esto, simplemente se identifican los términos semejantes en ambos resultados y se restan sus coeficientes correspondientes.</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Soluciones</B></div> <div>  <iframe width="853" height="480" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo1a1WvVncoAc1qSwVGHEXM2" frameborder="0" allowfullscreen></iframe>  </div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <B><IMG SRC="5a19b38f0.gif" border=0 width="947" height="399" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="5a1ab3810.gif" border=0 width="947" height="385" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="5a1bb3970.gif" border=0 width="947" height="407" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="5a1cb3970.gif" border=0 width="947" height="407" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="5a1db3840.gif" border=0 width="947" height="388" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="5a1eb3970.gif" border=0 width="947" height="407" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="5a1fb3b70.gif" border=0 width="947" height="439" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="5a20b3d00.gif" border=0 width="947" height="464" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="5a21b3cf0.gif" border=0 width="947" height="463" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="5a22b39c0.gif" border=0 width="947" height="412" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="5a23b9580.gif" border=0 width="697" height="344" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="5a24b3680.gif" border=0 width="947" height="360" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A 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